If I write out a book parametrization a Wankel engine and describing the chemistry and physics of the system necessary to make it turn, I have not implemented a Wankel engine, and I am in violation of no patents. It is a description of the engine, not an engine.

A mathematical description of an algorithm can be executed. It is the algorithm. The description is an implementation and any implementation is the description. There is literally no line between the two, the only thing that you can change is the notation in which you write it.

If you don't see the difference, you are just being obtuse. The difference is as plain the difference between physics and mathematics.